Question

What is the slant height x of this square pyramid? Express your answer in radical form.

Answer 1

Slant height is `3.464` meters.

Explanation:

Consider the triangular face, which appears as follows:

It is apparent that while side `AB=4` meters, `/_B=/_C=60^@`

Hence `/_a=180^@-60^@-60^@=60^@` and `DeltaABC` is an equilateral triangle.

and slant height `AD=x`, where `AD_|_BC`

Nowin `DeltasACD` and `ABD`, we have `AB=AC`, `/_B=/_C` and `AD=AD` and from `SSS` postulate we have `DeltaACD-=DeltaABD`

and hence `CD=BD` and as `BC=4` meters and hence `CD=BD=2` meters.

Now, we have from Pythagoras theorem

`AB^2=AD^2+BD^2`

i.e. `4^2=AD^2+2^2`

or `16=AD^2+4`

i.e. `AD=12`

and `AD=sqrt12=3.464` meters

Hence, slant height is `3.464` meters.